APR 9 1919 



A LEAD STANDARD CELL AND A DETER 

MINATION OF THE POTENTIAL OF 

THE LEAD ELECTRODE 



DISSERTATION 



PRESENTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE 

OF DOCTOR OF PHILOSOPHY IN THE GRADUATE SCHOOL OF 

THE OHIO STATE UNIVERSITY 






\ : 5 V' ... K a I T V 



^ 



BY 
GEBHARD STEGEMAN 



Columbus, Ohio 
1917 



A LEAD STANDARD CELL AND A DETER- 

MINATION OF THE POTENTIAL OF 

THE LEAD ELECTRODE 



DISSERTATION 



PRESENTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE 

OF DOCTOR OF PHILOSOPHY IN THE GRADUATE SCHOOL OF 

THE OHIO STATE UNIVERSITY 



BY 
GEBHARD STEGEMAN 



Columbus, Ohio 
1917 



A LEAD STANDARD CELL AND A DETERMINATION OF THE POTENTIAL 
OF THE LEAD ELECTRODE. 

I. Reason for the Investigation. 
II. Preparation of Materials. 

III. Apparatus. 

(a) Thermostat. 

(b) Thermometer. 

(c) Standard Cell. 

(d) Potentiometer. 

(e) Galvanometer. 
(/) Battery. 

IV. Results. 

(a) Preparation of the Standard Cell and a Discussion of the Results Ob- 

tained. 

(b) Outline of the Method Employed in the Determination of the Potential 

of the Lead Electrode. 
V. Summary. 
VI. References. 



I. Reason for the Investigation. 

A series of investigations has been in progress in this laboratory for 
some time, having for its object a study of the applicability of the measure- 
ment of electromotive force to the determination of the transition tem- 
peratures of hydrated salts. 

This method first suggested by Callender and Barnes, 1 and later de- 
veloped by Geiger, 2 depends upon the change in slope of the solubility 
curve of a salt accompanying the change from one hydrate to another. 
Since the electromotive force of a cell in which the hydrated salt com- 
prises a part is a function of the solubility of the salt, any change in the 
solubility curve of that salt will have a noticeable effect upon the electro- 
motive force. If the electromotive force of such a cell is plotted against 
the temperature, the slope of the curve obtained will undergo a change 
at the transition temperature of the salt, and by measuring the electro- 
motive force at different temperatures the transition temperature of the 
salt may be determined. For example, in the Clark cell, the salt which 
is stable up to 38. 2 2 is zinc sulfate heptahydrate (ZnSO 4 .7H 2 O). This 
salt changes to the hexahydrate (ZnSO4.6H2O) at 38.2, and since at 
this temperature both salts have the same solubility, the voltages of 
two cells containing, respectively, the heptahydrate and the hexahydrate 
would be identical. At no other temperature would this condition pre- 
vail. The fact that salts frequently remain in a metastable condition 
beyond the transition temperature does not affect the accuracy of the 
method, since by plotting the electromotive force against the tempera- 
ture two curves are obtained depending upon which salt is present in the 
cell, and the point of intersection of the two curves, representing the 
point of equal solubility will be the transition temperature. 

A cell used in the determination of the transition temperature of the 
salt comprising a part of that cell, must have the negative electrode com- 
posed of some metal which does not decompose water to an extent suffi- 
cient to affect the constancy of the electromotive force. The metals used 
in such cells have been chiefly zinc and cadmium, and the electrode must 
in general liberate an ion similar to that liberated by the salt in question. 
This requirement has prevented the determination of the transition 
temperature of a salt such as sodium sulfate decahydrate (Na 2 SO4.ioH 2 O), 
since a sodium electrode would decompose water so readily, that it would 
not show a constant electromotive force. The same type of cell which 
would allow a determination of the transition temperature of a salt such 



as zinc sulfate heptahydrate, could, therefore, not be used in the de- 
termination of the transition temperature of sodium sulfate decahydrate 
(Na 2 SO 4 .ioH 2 O). 

In the hope of finding a type of cell which would avoid these difficulties 
and still permit the determination of the transition temperature of a salt 
such as sodium sulfate decahydrate, Na 2 SO 4 .ioH 2 O, the following type 
of cell was prepared: 

Pb amalgam PbSO 4 Na 2 SO 4 . ioH 2 O Hg 2 SO 4 Hg 
The chemical reaction occurring in the cell is 

Pb + Hg 2 SO 4 > PbSO 4 + 2Hg. 

This reaction does not show that the sodium sulfate is in any way 
connected with the reaction, but the electromotive force of such a cell 
is a function of the solubility of the lead sulfate (PbSO 4 ), and this is in 
turn dependent upon the amount of sodium sulfate in the solution. It 
was thought that the mass effect of the common ion SO 4 would cause 
sufficient change in the amount of lead sulfate dissolved to make a per- 
ceptible change in the electromotive force. Thus by raising the tempera- 
ture of the cell and thereby increasing the amount of sodium sulfate in 
solution, a subsequent decrease in the amount of the lead sulfate dissolved 
should cause a change in the electromotive force. At the transition 
temperature of the sodium sulfate, the solubility of the hydrated salt is 
the same as the solubility of the anhydrous salt, and consequently the 
electromotive force of the cell should have a definite value no matter which 
salt is present. 

It is essential for accurate determinations of the transition temperatures 
of salts by this method that the temperature coefficient of the cell be 
rather large. Reference to Table I will show that the temperature co- 
efficient of a cell made with an unsaturated amalgam is very small and 
for this reason the study of these cells with refernece to the transition 
temperatures of salts was discontinued. The freedom from variation 
of the electromotive force of this type of cell suggested further study with 
the following aims: 

(1) The determination of the condition under which the cell would be 
reproducible. 

(2) The use of the cell as an indirect method to determine the poten- 
tial of the lead electrode. 

(i) It was found that the lead amalgam used was an unsaturated 
one, that is, the percentage of lead was below that required to saturate 
the mercury with lead. Lead is soluble in mercury to the extent of 



about 1.5% by weight and any attempt to dissolve more lead in the 
mercury results in the formation of the compound (Pb 2 Hg). This com- 
pound is in equilibrium with a saturated amalgam. The active part of 
the electrode is the liquid amalgam and any decrease in the percentage 
of lead during the action of the cell is compensated by the solution of 
the compound (Pb 2 Hg), which tends to restore the previously existing 
equilibrium. 

In order to make a lead electrode with a reproducible electromotive 
force, a saturated amalgam is obviously the concentration to be sought, 
and this concentration may be obtained by having an excess of the com- 
pound Pb 2 Hg present at all times. From a study of the electromotive 
force of lead amalgams, Puschin 3 has concluded that the potential of such 
amalgams has a constant value when the concentration of lead is between 
the limits of 1.8 and 66%. An electrode consisting of lead and mer- 
cury with the lead concentration between these limits should, therefore, 
be reproducible, and a study of the most convenient concentration which 
would give a reproducible electromotive force was undertaken. 

II. Preparation of Materials. 

(1) Lead nitrate. A sample of Baker's C. P. lead nitrate was twice 
recrystallized.from pure water and served as the source of lead for the 
amalgams. 

(2) Lead amalgams. The amalgams were prepared in two ways: 

(a) A solution of lead nitrate, containing a trace of nitric acid and 
about 10% of lead nitrate, was electrolyzed in a platinum dish which 
served as the cathode, with a thin plate of platinum foil serving as the 
anode. The current used was never more than one- tenth of an ampere 
while the voltage was one and one-half volts. The precipitated lead 
was washed with water while adhering to the dish and was readily re- 
moved. To dry the crystals completely they were washed with a solu- 
tion of alcohol-ether and the last traces of the liquid were removed by 
a clean blast of dry air. The dry crystals were then melted in a hard glass 
flask in an atmosphere of hydrogen to prevent oxidation. The metallic 
button thus obtained was preserved for use in the preparation of the 
amalgams. 

Suitable quantities of lead and mercury were weighed in porcelain 
crucibles and the lead which was cut into small pieces was added to the 
mercury. The crucible was then warmed somewhat to promote the 
solution of the lead and the amalgam formed was stirred with a glass 



8 

rod till it appeared to be homogeneous. To prevent undue oxidation 
during the heating, the amalgam was protected by a coating of liquid 
paraffin. When the amalgam was to be transferred to the cell, the thin 
coating of paraffin was removed with a spatula, and the amalgam was 
placed in the cell by means of a small-bore pipette since the amalgam 
is liquid when warm. Upon cooling a granular compound separates 
out, which has been shown by Fay and North 4 to have the composition 
Pb2Hg. They have also shown that this compound exists in equilibrium 
with the liquid part of the amalgam even though the percentage of lead 
vary from two to fifty-five per cent. When this equilibrium has been 
established the liquid and the solid phase have the same potential which 
should, therefore, be constant within these limits at any one temperature. 
(6) The amalgam was also prepared electrolytically by the electrolysis 
of a ten percent solution of lead nitrate with a weighed amount of mercury 
serving as the cathode. A coulometer in the circuit served to show the 
amount of lead deposited in the mercury. When the electrolysis had 
proceeded to the desired point, the solution of lead nitrate was decanted 
from the amalgam which was then thoroughly washed with distilled water. 
There seems to be little to choose between the two methods as both produce 
amalgams of identical voltages. The electrolytic method is perhaps the 
more convenient of the two, since it is easily controlled and is not attended 
by any oxidation such as is likely to occur when a lead amalgam is heated. 

(2) Sodium sulfate (Na 2 SO 4 .ioH 2 O). 

A supply of C. P. anhydrous sodium sulfate was dissolved in pure distilled 
water and the crystals of sodium sulfate formed were twice recrystallized. 
The salt was kept in a slightly moistened condition to prevent efflorescence. 
The presence of a trace of ferric ion present in the original salt could not be 
detected after the second recrystallization. 

(3) Mercurous sulfate (Hg 2 SO4). 

The preparation of this very important compound was carried out with 
the greatest attention possible. The method employed by Hulett 5 , an 
authority on the construction of standard cells, was carefully followed. 
This consists in electrolyzing a solution of sulfuric acid of specific gravity 
1.15, in a glass dish with an anode of pure mercury. This method has the 
distinct advantage that the precipitated mercurous sulfate is very intimately 
mixed with minute globules of mercury. This intimate mixture of salt 
and metal is a protection against the formation of any mercuric salt, since 
the metallic mercury acts as a very effective reducing agent. The presence 
of mercuric salts must be avoided since they are so much more soluble 
than the mercurous salts and the potential existing between the mercury 



and a solution of its salts, depends upon the concentration of mercury 
ions. The salt prepared by this method was preserved in a dark colored 
bottle under the solution from which it was prepared. 

(4) Lead Sulfate: 

This salt was prepared by precipitation from a dilute solution of lead 
nitrate by means of dilute sulfuric acid. In order to remove any occluded 
lead nitrate, the precipitate was boiled four times with successive portions 
of distilled water which was decanted after the precipitate had settled. 
This salt was kept in a glass-stoppered bottle under dilute sulfuric acid 
to prevent the hydrolysis which might occur if kept in contact with pure 
water. 

(5) Mercury: 

Ordinary mercury was stirred for two days in contact with dilute nitric 
acid, and was then distilled under reduced pressure according to the 
method of Hulett. 6 After the second distillation no oxides of any kind 
remained either in the distilling flask or the receiver. The mercury thus 
purified maintained its mirror surface indefinitely. 

(6) The Paste: 

The mercurous sulfate prepared as described was washed until free from 
the acid under which it was preserved. This was very conveniently done 
in a Gooch crucible with a small disk of filter paper accurately fitting the 
bottom. The mercurous sulfate was poured into the crucible and the acid 
drawn off by suction. The acid remaining upon the salt was removed by 
five or six small portions of a saturated solution of sodium sulfate. Each 
portion of the washing solution was removed as completely as possible 
by suction before adding a new portion. This kind of procedure prevents 
the troublesome hydrolysis of the mercurous sulfate which occurs in 
aqueous solution according to the following equation : 

2 Hg 2 S0 4 + 2HOH^1 |Hg2SO 4 .2Hg(OH)] + H 2 SO 4 

This hydrolysis must be avoided as the acid produced has a marked effect 
upon the potential difference existing between the mercury and the solu- 
tion of mercurous sulfate. 

The lead sulfate prepared according to the previous description was 
washed free from the acid under which it was kept, in a way analogous to 
that described in the case of the mercurous sulfate. A mixture consisting 
of equal portions of mercurous sulfate, lead sulfate, and sodium sulfate, 
was stirred till it appeared well mixed and enough of a saturated solution 
of sodium sulfate was added to make a thin paste. 

(7) Preparation of the Cell: 



10 

The H type of cell appealed to be the best adapted to the work con- 
templated. The glass part of the cell was prepared by joining together 
two "culture-tubes" such as are used in bacteriological work at about four 
cms. from the closed end. The glass of which these tubes are made is 
easy "to work" and does not crack on cooling. Two small-bore glass 
tubes with platinum wires sealed into one end passed through the stoppers 
placed in the open ends of the cell, and served to connect the cell with the 
potentiometer. 

When the cell was ready to be filled, some of the pure distilled mer- 
cury was placed in one leg of the glass vessel by means of a small-bore 
pipette. Some of the paste consisting of an intimate mixture of mer- 
curous sulfate, lead sulfate, and sodium sulfate was then placed upon 
the mercury to a depth of about one cm., also by means of the pipette. 
The lead amalgam was then placed in the other leg of the cell in a similar 
manner. Most of the amalgams used were liquid with a small amount of 
the solid phase in equilibrium with it. By warming this amalgam slightly, 
the solid phase readily dissolved in the liquid phase and was then easily 
placed in the cell as a homogeneous liquid. Upon cooling, the solid phase 
again separated out so that a saturated amalgam was always present. 
In the case of amalgams containing a higher percentage of lead, the pipette 
used to transfer the amalgam from the container to the cell was warmed 
in the Bunsen flame, and the warm amalgam was drawn into it. 
Before the temperature had fallen to the solidification point, the amal- 
gam was quickly placed in the cell. In this way only the pure amalgam 
containing no oxide was transferred to the cell. This amalgam was then 
covered immediately with a mixture consisting of solid lead sulfate inti- 
mately mixed with finely powdered sodium sulfate. This mixture was 
made into a thin paste by adding a little water saturated with both lead 
sulfate and sodium sulfate. The cell was then filled up to the cross arm 
with an intimate mixture of both lead sulfate and sodium sulfate. Enough 
of a solution saturated with both these salts was then added so as to fill 
the cell above the cross arm. The glass leads containing the platinum 
wires were then placed in position, and cork stoppers provided with a hole 
for the glass tubes placed in the ends of the tubes. Two or three such 
cells were then tied in a bundle and took up but little room in the thermo- 
stat. 

III. Apparatus. 

(a) Thermostat. 

Two thermostats electrically heated and regulated to 0.01 were avail- 
able and served to keep the cells at any desired temperature. One of 



II 

these thermostats was regulated at 25.00 and the Weston cell serving as 
a reference was always kept at this temperature. 

(6) Thermometer. 

The thermometer was graduated in tenths of a degree and had been 
standardized by the Bureau of Standards at Washington. By the aid 
of a small eye-glass the temperature could be accurately read to one- 
hundredth of a degree. 

(c) Standard Cell. 

The Standard Cell was of the Weston unsaturated type procured from 
the Weston Laboratory. The one used for constant reference was No. 3,408 
and had a voltage of 1.01865 volts at 25 C. It was frequently compared 
with a similar cell, No. 3,539, which was recently procured. It was 
constantly kept in the thermostat regulated at 25.00. 

(d) Potentiometer. 

The potentiometer used to measure the voltages of the cells was a 
Leeds and Northrup instrument reading to o.ooooi volt. 

(e) Galvanometer. 

A very sensitive Leeds and Northrup galvanometer was employed as 
a "Null instrument." This instrument was sensitive enough to detect 
a change of less than o.ooooi volt. 

(0 Battery. 

The source of current for the potentiometer was an ordinary "chloride 
accumulator" showing a voltage of about 2.10 volts. 

IV. Results. 

(a) Observations on cells prepared with unsaturated lead amalgams. 

(6) Observations on cells prepared with saturated amalgams. 

(a) All cells prepared according to the manner described were allowed to 
remain in the thermostat for about twelve hours before any readings 
were recorded. The first type of cell studied was prepared with an un- 
saturated lead amalgam as the negative electrode and contained approxi- 
mately 0.70% of lead. Since this percentage is below the saturation point 
of lead in mercury, the observed electromotive force is a function of the 
concentration of the lead in the amalgam. This type of cell exhibited some 
interesting features, however, namely, the constancy of voltage and the 
low temperature coefficient. 



12 

TABLE I. 

Observation on a Cell with a 0.703% Pb Amalgam. 
E. M. F. Time. Temp. 

0.95815 11/15/16 25.00 

0.95815 11/22/16 25.00 

0.95820 11/23/16 30.00 

0.95820 I2/ 5/16 30.00 

This type of cell has a temperature coefficient of +0.00001 volt. It 
is also interesting to note that the voltage increases with rise of tempera- 
ture, a property possessed by few voltaic cells, the most prominent one 
being the Daniel cell. 

Since these cells exhibit such a constant voltage it was interesting to 
see how well the observed values of voltage and temperature coefficient 
would agree with the theoretical value. The Gibbs-Helmholtz equation 
connects the heat of reaction of a cell with the electromotive force as 
follows : 

Q = NF(E TdEAfT)o.2 3 87 

In this equation Q = heat of reaction determined from thermochemical 
data. 

0.2387 is the conversion factor for electrical to heat energy 

E is the observed electromotive force. 

T is the absolute temperature. 

dH/dT is the temperature coefficient. 

N is the valence of the reacting metal. 

F is one Faraday or 96,550 coulombs. 

The reaction taking place in the cell is given by the equation Pb + Hg 2 SO 4 
> PbSO 4 + 2Hg. The reaction in this cell is very simple, and in mak- 
ing a comparison between observed and calculated values, no complica- 
tion is introduced, due to the heat of hydration of the salt formed, as 
is the case in the Clark and Weston cell. The heat of formation of lead 
sulfate from its elements at 18 as determined by Thomsen is 216,200 cals. 
The heat of formation of mercurous sulfate is given as 175,000 cals. The 
difference 41,200 cals. represents the heat liberated in the reaction. The 
heat of the reaction as determined by the Gibbs-Helmholtz equation is 
as follows: At 18.00 the e. m. f. of the cell under consideration is 0.95808 
and dH/dT = +0.00001. 

Therefore, Q = NF[o.958o5 291(0.00001) 30.2387 = 44,025 cals. 
However, the reaction occurring in the cell is not wholly represented 
by Pb + Hg 2 SO 4 > PbSO 4 + 2Hg, but is instead, Pb-amalgam + Hg 2 SO 4 
> PbS0 4 + 2 Hg. 



13 

Bronsted 7 has shown that a chain [Pb solid Pb salt Pb 0.72% amal- 
gam] gives a voltage (0.0051 + 0.000233*). 

Substitution of these values in the Gibbs-Helmholtz equation gives 
a value of 2,697 ca ^ s - f r the heat of solution of Pb in mercury to form 
a 0.72% amalgam at 18.00. 

Q = 0.2387 [0.0092 29 1 (0.000233) ]NF = 2,697 ca k. 
When a cell containing a lead electrode composed of an unsaturated 
amalgam of 0.72% Pb is in action, 2,697 cs ^ s - of neat will be liberated 
for every atomic weight of lead going into solution. 44,025 2,697 = 
41,328 cals. would, therefore, be the free energy of the reaction as com- 
pared with 41,200 cals. obtained in a thermochemical way. 

Attention was next directed toward a verification of the assertion that 
between certain limits of concentration the potential of lead amalgams 
is independent of the concentration of lead. As before mentioned, Puschin 3 
has shown that amalgams of lead have the same potential between the 
limits of 1.8-66% of lead. Several cells were prepared with amalgams 
varying in concentration from 2 to 10% of lead, 10% being about the 
limit for convenient handling since amalgams with a higher percentage 
of lead are quite solid at ordinary temperatures. The best results so far 
obtained have been with amalgams ranging from a percentage of lead of 
2.5 to 3.9% as shown by the following table: 

TABLE II. 

Temp. 

25-00 

25-00 

25.00 

25-00 

25-00 

18.00 

18.00 

30.00 

30.00 

25.00 

While these cells have different concentrations of lead in the amalgams, and 
did not agree well at first, they have both assumed the same value, and 
appear to remain so except for a very gradual decrease in voltage, a property 
often encountered in such good cells as the cadmium standard cell. 

To test the reproducibility of these cells, three cells were prepared on 
Feb. 9, 1917, in the usual way with the exception that the amalgams were 
prepared electrolytically. The voltages obtained follow : 



Cell I 


Cell II 








Amalgam 2.6% Pb. 


Amalgam 3.5% Pb. 


Time. 





.96470 





96453 


Dec. 


12, 


I9l6 


O 


96465 


O 


96470 


Jan. 


18, 


1917 


O 


96465 


O 


. 96468 


Feb. 


2, 


1917 


0.96463 


O 


. 96464 


Mar. 


2, 


1917 


O 


96463 





. 96464 


Apr. 


6, 


1917 


O 


96342 


O 


96343 


Apr. 


15, 


1917 





96343 


O 


96343 


Apr. 


18, 


1917 


O, 


96550 


O 


96552 


Apr. 


19, 


1917 


O, 


96550 





96552 


Apr. 


21, 


1917 


0, 


96463 


O 


96463 


May 


15, 


1917 



Cell I. 


Cell II. 


Cell III. 


Temp. 


o . 96465 


0.96461 


. 96464 


25.00 C 


. 96465 


O . 96462 


o . 96463 


25.00 


o . 96465 


O . 96462 


. 96463 


25.00 


O . 96464 


0.96461 


o . 96462 


25.00 



14 
TABLE III. 

% of lead 
in amalgam. Date. 

3.10% 2/12/iy 
2/15/17 
2/18/17 
3/I2/I7 

A comparison with the other two cells described shows that all five 
cells have the same voltage within a few hundredths of a millivolt, thus 
making the cell reproducible within that limit. Since the cell shows a 
voltage that is quite constant and appears to be reproducible to a few 
hundredths of a millivolt, it is possible to make a determination of the 
free energy of the reaction occurring in the cell using the values that have 
been determined as a basis. As previously indicated, this may be done 
by means of the Gibbs-Helmholtz equation: 

Q = NF(E TdE/dT)o.2 3 87 

A very careful determination of the value dE/dT is necessary for an ac- 
curate determination of the value of Q. The great accuracy required in 
this operation will be evident from a consideration of the equation. The 
factor o!E/dT is multiplied by the absolute temperature T, in this case 
291, and the effect of a small error in the value of dH/dT is thus con- 
siderable. To determine the value d~E/dT, we may proceed as follows: 
The electromotive force at any temperature may be expressed as a func- 
tion of the value of the electromotive force at any given temperature. 
Thus we may write, 

E T = E 25 + a(T - 25) + 6(T - 25)'. (I) 

The last term in the equation is necessary because the variation of the 
electromotive force with the temperature is not always a straight line 
function. Referring to equation (I), it is evident that it consists of an 
equation with two unknown quantities, "a" and "b." To evaluate these 
constants it is necessary to know the value of the electromotive force at 
three different temperatures. There will then be two simultaneous equa- 
tions from which the value of the constants may be determined. The 
temperatures chosen for observation were 30, 25 and 18. Table II gives 
the values obtained at these three temperatures, and a substitution of 
these values in equation (I), gives two simultaneous equations of the fol- 
lowing form : 

0.96343 = 0.96463 + a( 7) + 6(49) 

0.96551 = 0.96463 + 0(5) + 6(25) 



15 

The solution of these two simultaneous equations gives a value of 
+0.000174 for "a" while "b" has the value +0.00000038. Equation (I) 
then assumes the form: 

ET = 0.96463 + o.oooi74(T 25) + o.oooooo38(T 25)2 

This equation reproduces the values found at 30 and 18, and by 
differentiating this equation the value for dH/dT at 18.00 is found to be 
+0.000169. Substitution of the values found in the Gibbs-Helmholtz 
equation gives the equation the following form: 

Q = 46092(0.96343 291(0.000169)] = 42,139 cals. 

However, the reaction occurring in the cell is not wholly represented by 
Pb + Hg 2 SO 4 > PbSO 4 + 2Hg, but by Y 2 Pb 2 Hg + Hg 2 SO 4 > PbSO 4 + 
2V2Hg. The heat of solution of lead in mercury to form the compound 
Pb 2 Hg must, therefore, be determined before the actual heat of the reac- 
tion occurring in the cell can be determined. Bronsted 7 has determined 
the electromotive force of a chain [Pb solid PbCl 2 PbHgm] and 
has found it to be (0.0051 + 0.000233*) volt. These values when substi- 
tuted in the Gibbs-Helmholtz equation give a value of 2,697 cals. as the 
heat of solution of lead in mercury to form a dilute amalgam as previously 
indicated. The amalgam used in the cell under consideration consists of 
the compound Pb 2 Hg in equilibrium with a saturated amalgam and the 
heat of reaction when lead dissolves to form this compound would not 
be the same as that occurring when lead goes to form a dilute amalgam. 
The heat of reaction when the compund Pb 2 Hg is formed was determined 
indirectly by Luther. 8 The chain [Pb 2 Hg PbCl 2 PbHg dilute 
amalgam] was found to give an e. m. f. (0.00016 + 0.000191*)- At 18 
the heat of reaction calculated from the Gibbs-Helmholtz equation is 
2,115 cals. The difference between ( 2,697 and 2,115) amounting to 
582 cals. must be the heat of reaction when lead dissolves in mercury 
to form the compound Pb 2 Hg. The value of the heat of reaction occurring 
in the cell under consideration will be too high by this amount, and the 
true value for the reaction Pb + Hg 2 SO 4 > PbSO 4 + 2Hg will be 
41,557 cals., against 41,200 cals. obtained thermochemically. This is 
an error of approximately 0.86%, almost as good an agreement as found 
in the Clark cell. 

It appeared interesting to try the effect of the substitution of zinc sulfate 
heptahydrate for the sodium sulfate decahydrate in the cell. Some cells 
were accordingly prepared in the same way as that described with the ex- 
ception that zinc sulfate was used instead of sodium sulfate throughout. 
The values obtained follow: 



i6 
TABLE IV. 

Cell I. Cell II. Date. Temp. 

0.96487 0.96485 3/ 6/17 25.00 

0.96487 0.96485 3/12/17 25.00 

0.96487 0.96485 3/I5/I7 25.00 

0.96364 0.96362 3/16/17 18.00 

0.96364 0.96362 3/18/17 18.00 

0.96563 0.96561 3/I9/I7 30.00 

0.96563 0.96561 3/20/17 30.00 

0.96487 0.96485 3/28/17 25.00 

It is interesting to note that in spite of the larger solubility of the zinc 
sulfate the voltage of a cell prepared in this way is only 0.00023 volt higher 
than that of a cell in which sodium sulfate is used. The voltage of this 
cell at any temperature may be calculated by means of the equation: 

ET = 0.96486 + o.oooi62(T 25) o.ooooo2(T 25)2 
This equation gives a value of +0.000190 for dE/dT at 18.00. Substitu- 
tion of the values found in the Gibbs-Helmholtz equation gives Q = 
46092(0.96363 291(0.000190)] = 41,867 cals. Subtracting 582 cals. 
from this value as previously indicated gives the value 41,285 cals. as the 
free energy of the reaction Pb + Hg 2 SO 4 > PbSO 4 + 2Hg. This is 
an error of about 0.19%, when compared with the value obtained by 
Thomsen in a thermochemical way. 

(6) The constancy of the voltage of a lead amalgam such as was em- 
ployed in the preparation of the cell previously described, suggested that 
such an amalgam might be used in a measurement of the potential of the 
lead electrode, provided the difference in voltage between such an amalgam 
and a solid lead electrode were accurately known. 

Several investigations of the lead electrode 9 have been made at various 
times but the data is not in agreement. Getman 9 describes a measurement 
of the potential of a solid lead electrode immersed in a saturated solution 
of lead chloride. This electrode was prepared by precipitating lead elec- 
trolytically upon platinum from a solution of lead nitrate. Fluctuations 
in voltage amounting to as much as 0.0022 volt were observed by Getman. 
It was thought possible that some action between the lead and the solution 
of the chloride might be taking place such as is the case in a solution of 
lead nitrate. 

The plan of measuring the potential of lead against a solution saturated 
with lead sulfate and sodium sulfate appeared promising, judging from the 
constant results obtained in the standard cell. Several cells were accord- 
ingly prepared, identical in every respect with those described, except that 
a solid lead electrode was substituted for the amalgam. This solid elec- 



trode was prepared by precipitating lead upon a heavy platinum wire ac- 
cording to the method described by Getman. 9 These cells while they did 
not agree exactly showed reasonable constancy for at least thirty hours 
after which a gradual decrease in voltage became apparent. The voltages 
follow : 

TABLE V. 

Cell I. Cell II. Cell III. Cell IV. Temp. Time in hrs 

0.96990 0.96967 0.96970 0.96972 25.00 2 

0.96991 0.96967 0.96971 0.96970 25.00 5 

0.96990 0.96968 0.96970 0.96970 25.00 10 

0.96990 0.96966 0.96970 0.96969 25.00 I 8 

0.96988 0.96965 0.96969 0.96969 25.00 30 

The mean of these values is 0.96974 volts. The voltage of a cell prepared 
with an amalgam instead of a solid electrode is 0.96463 volt. The differ- 
ence between the two, 0.00511 volt, represents the potential difference 
existing between a solid lead electrode and a 3-4% lead amalgam. 

The activity of the lead ion liberated by lead sulfate in a solution satu- 
rated with sodium sulfate would be very difficult to determine with any 
accuracy, and since this value must be known in order to calculate the 
normal electrode potential, the plan of measuring the potential difference 
between a 3-4% amalgam and a solution saturated with lead chloride 
was followed. 

Since the solubility of lead chloride at 25.00 is 0.0388 mol. per liter, the 
activity of the lead ion may be determined with some degree of accuracy. 
At this dilution Noyes and Toabe 11 give the value of 56.2% for the ex- 
tent of dissociation of lead chloride, but this result is based upon conduc- 
tivity measurements, and may, therefore, be subject to a slight error. 
This error will not affect the accuracy of the measurements described, 
as a simple calculation will give the normal electrode potential, in case a 
revision of the activity of the lead ion is found necessary. Since this 
work was done an article has appeared by Lewis and Brighton, 12 in which 
they express the hope that they will be able to determine with greater 
certainty the activity of the lead ion at this dilution. 

Attention was, therefore, directed toward the determination of the 
potential of a 3-4% amalgam of lead, against a saturated solution of lead 
chloride. All the measurements were made against a battery of three 
tenth-normal calomel electrodes. Some difficulty was experienced at 
first in preparing calomel electrodes that did not vary in voltage. Finally 
the preparation of calomel by the electrolysis of a normal solution of 
hydrochloric acid, using a mercury anode according to the method de- 



i8 

scribed by Ellis, 13 produced calomel which gave excellent results in the 
standard electrodes. The calomel was washed free from hydrochloric 
acid by washing it in a Gooch crucible with a tenth-normal solution of 
potassium chloride, before being used in the cells. The potassium chloride 
used had been twice recrystallized and heated, and the solution was thor- 
oughly saturated with calomel before use. No difference in potential 
was apparent between the three standards and each lead half-cell was 
measured against the three standards in turn. 

The half -cell (Pb2Hg PbCl2 sat. solution) was prepared by covering 
the 3-4% amalgam of lead with about one cm. of solid lead chloride which 
had been recrystallized three times. 

The cell was then filled with a solution of lead chloride saturated at 
about 30.00 thus insuring a saturated solution at 25.00 at which tempera- 
ture all measurements were made. Connection with the standard electrode 
was made by means of a saturated solution of potassium chloride. These 
lead cells exhibited a very constant voltage during the sixty -hour observa- 
tion period, though there was a slight difference between the different 
cells. The following values are the means of about ten measurements 
taken of the voltages of the cells during a sixty -hour period. 

TABLE VI. 
Voltage of the Chain (Pb 2 Hg-PbCl 2 -KCl-o. i N KCl-Hg 2 Cl 2 -Hg) 

Amalgam I. Amalgam ll. Amalgam III. Amalgam IV. Temp. 

0.5138 0.5137 0.5135 0.5136 25.00 

The voltage is indicated only to tenths of a millivolt because the re- 
sistance of the chain was large enough to make the fifth decimal uncertain. 
The mean of these values, 0.51365, is, therefore, taken as the voltage of 
the chain under consideration. Adding the value, 0.0051 volt, which is 
the difference in potential between the amalgam and a solid lead elec- 
trode, gives 0.5187 as the voltage of the chain 

Pb solid PbCl 2 KC1 o.i N KC1 Hg 2 Cl 2 Hg. 

It is now possible to calculate the normal electrode potential of lead by 

means of the equation 14 

E = E (RT/ 2 FlnC) 

in which E = 0.5187, 

E = normal electrode potential, 

R, T and F have the usual values, 

and C = concentration in mols. of lead ions present. 



19 

The degree of dissociation of lead chloride in a saturated solution is 
taken as 56.2% and the equation, therefore, assumes the following form: 

0.5187 = E RT/2F In (0.0388 X 0.562) = 0.4696 

This is the value of the normal electrode potential of lead measured against 
the tenth-normal calomel electrode at 25.00. 

V. Summary. 

A lead standard cell has been prepared which has been found to possess 
a constant voltage which is reproducible to within a few hundredths of 
a millivolt. The voltage of the cell is conveniently large to permit its 
use as a standard. 

A determination of the potential of the lead electrode against the tenth- 
normal calomel electrode has been made and found to be 0.4696 at 25.00. 
This value may be subject to a slight change when the activity of the 
lead ion in a saturated solution of lead chloride becomes more accurately 
known. 

The author wishes to take this opportunity to thank Dr. William E- 
Henderson for his interest and his many timely suggestions. 

VI. References. 

1. Proc. Roy. Soc., 62, 117. 

2. Dissertation, O. S. U., 1916. 

3. Z. anorg. Chem., 36, 201 (1903). 

4. Am. Chem. J., 25, 216 (1901). 

5. Phys. Rev., 32, 334 (1906). 

6. Ibid., 33, 33 (1907). 

7. Z. phys. Chem., 56, 645 (1906). 

8. Z. Elektrochem., 17, 293 (1911). 

9. (a) Ibid., 7, 477 (1900-01). 

(b) Ibid., 10, 77 (1904). 

(c) Z. phys. Chem., 56, 645 (1906). 

(d) J. Chem. Soc., 38, 792 (1916). 

10. J. Am. Chem. Soc., 25, 469 (1903). 

11. Ibid., 39, 1537 (191?)- 

12. Ibid., 39, 1906 (1917). 

13. Ibid., 38, 737 (1916). 

14. Ibid., 35, i (1913). 

ADDITIONAL REFERENCES. 
Z. Elektrochem., 2, 68 1 (1905). 

J. F. Spencer, "Ueber die electromotorische Wirksamkeit verdiinnter Amalgame." 
Am. Chem. J., 50, 396 (1913). 
C. N. Myers and S. F. Acree, "A Study of Calomel Electrodes." 



2O 

Z. phys. Chem., 47, 146 (1904). 
Ludwig Sauer, "Bezugselektroden." 
Z. phys. Chem., 35, 333 (1900). 

W. Ostwald, "Uber die absoluten Potentiale der Metalle." 
Z. phys. Chem., 24, 46 (1897). 

T. W. Richards, "Ueber den Temperaturkoeffizienten des Potentials der Kalo- 
melelektrode mit verschiedenen gelosten Elektrolyten." 
Z. phys. Chem., 72, 165 (1910). 

T. W. Richards, "Elektrochemische Untersuchung fliissiger Amalgame." 
Trans. Am. Electrochem. Soc., 14, 65 (1908). 
G. A. Hulett, "Equilibria in Standard Cells." 



AUTOBIOGRAPHY. 

I was born near Holland, Michigan, June 14, 1890. My early education 
was such as the country school afforded at the time. From 1904 to 1908, 
I was enrolled in the Hope College Preparatory Department, finishing 
the course in 1908. The following year I spent in the study of music at 
the Hope College Conservatory of Music. My interest in less artistic 
pursuits prompted me to enroll as a Freshman in Hope College, in Sep- 
tember, 1909, and during that year I developed an interest in chemistry 
under the teaching of Dr. A. T. Godfrey, head of the Chemistry Depart- 
ment. I was graduated in June, 1913, receiving the degree of Bachelor 
of Arts. The next four years I spent in pursuit of the degree of Doctor 
of Philosophy at the Ohio State University, serving as an assistant in the 
Department of Chemistry while fulfilling the requirements of the degree 
which I received in June, 1917. 



UNIVEESITY OF CALIFOENIA LIBRARY, 
BEEKELEY 



Books not returned on time are subject to a fine of 

f n OC 1 P nn V lume , after *> third da y overdue increasing 
to $1.00 per volume after the sixth day. Books no t in 

aSSStoSyi ? 6 Tenew ^ if application is made before 
expiiation of loan period. 



20m-ll,'20 



' U U I 




390600 



UNIVERSITY OF CALIFORNIA LIBRARY 



